Question

A train starts from station P at a speed of 60 kmph and arrives at station Q in 45 minutes. If its speed is reduced by 6 kmph, how much more time will that train take to return from station Q to arrive at station P?

• A. 4 minutes
• B. 5 minutes
• C. 6 minutes
• D. 8 minutes

Hint:

When distance is fixed, time is inversely proportional to speed. A decrease in speed always increases the travel time.

Answer 1

The Correct Option is B

Concept: Distance remains constant for both journeys. Therefore, first calculate the distance using the original speed and time, and then determine the new travel time using the reduced speed.

Step 1: Calculating the distance between stations P and Q.
Speed of train \[ =60\ \text{kmph} \] Time taken \[ =45\ \text{minutes} =\frac{45}{60} =\frac{3}{4}\ \text{hour} \] Distance \[ =\text{Speed}\times\text{Time} \] \[ =60\times\frac{3}{4} =45\ \text{km} \]

Step 2: Finding the return time with reduced speed.
Reduced speed \[ =60-6 =54\ \text{kmph} \] New time \[ =\frac{45}{54}\ \text{hour} =\frac{5}{6}\ \text{hour} \] Converting into minutes, \[ \frac{5}{6}\times 60 =50\ \text{minutes} \]

Step 3: Calculating the extra time.
Original time \[ =45\ \text{minutes} \] New time \[ =50\ \text{minutes} \] Extra time \[ =50-45 =5\ \text{minutes} \] {5 minutes}